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Simplifying x2 + 63x + -51 = 0 Reorder the terms: -51 + 63x + x2 = 0 Solving -51 + 63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 63x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 63x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 63x + x2 = 0 + 51 63x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 63x + x2 = 51 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = 51 + 992.25 Reorder the terms: 992.25 + 63x + x2 = 51 + 992.25 Combine like terms: 51 + 992.25 = 1043.25 992.25 + 63x + x2 = 1043.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 1043.25 Calculate the square root of the right side: 32.299380799 Break this problem into two subproblems by setting (x + 31.5) equal to 32.299380799 and -32.299380799.Subproblem 1
x + 31.5 = 32.299380799 Simplifying x + 31.5 = 32.299380799 Reorder the terms: 31.5 + x = 32.299380799 Solving 31.5 + x = 32.299380799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 32.299380799 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 32.299380799 + -31.5 x = 32.299380799 + -31.5 Combine like terms: 32.299380799 + -31.5 = 0.799380799 x = 0.799380799 Simplifying x = 0.799380799Subproblem 2
x + 31.5 = -32.299380799 Simplifying x + 31.5 = -32.299380799 Reorder the terms: 31.5 + x = -32.299380799 Solving 31.5 + x = -32.299380799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -32.299380799 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -32.299380799 + -31.5 x = -32.299380799 + -31.5 Combine like terms: -32.299380799 + -31.5 = -63.799380799 x = -63.799380799 Simplifying x = -63.799380799Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.799380799, -63.799380799}
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